A combined first‐ and second‐order approach for model predictive control

This article presents a simple iterative method that combines first‐ and second‐order approaches for linear model predictive control (MPC). Approximate value functions requiring only first‐order derivatives and incorporating fixed second‐order information are employed, which leads to a method that splits the MPC problem into subproblems along the prediction horizon, and only the states and costates (Lagrange multipliers corresponding to the state equations) are exchanged between consecutive subproblems during iteration. The convergence is guaranteed under the framework of the majorization minimization principle. For efficient implementation, practical details are discussed, and the performance was assessed against both first‐ and second‐order methods with two numerical experiments. The results indicate that the proposed method can obtain a moderately accurate solution with a small number of cheap iterations.